Part b) only. Use Julia in Jupyter Notebook please.

6. When computing the determinant of a matrix by hand, it's common to use cofactor expansion and apply the definition recursively. But this is terribly inefficient as a function of the matrix size. (a) Explain using determinant properties why, if A=LU is an LU factorization, det(A)=U11U22Unn=i=1nUii. (b) Using the result of part (a), write a function determinant ( A ) that computes the determinant using Function 2.4.6. Test your function on at least two nontriangular 55 matrices, comparing your result to the result of the standard det function. LU factorization (not stable)